kinetic plasma processes in the solar corona. - indico...
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Kinetic plasma processes in the solar corona
• Basic assumptions of collisional transport theory• Kinetics of coronal (solar wind) heating through
Landau/cyclotron damping of plasma waves• Solutions of the Vlasov-Boltzmann equation• Model velocity distributions in the corona• Kinetic plasma instabilities in the solar wind
Eckart MarschMax-Planck-Institut für Sonnensystemforschung, Germany
Kinetic processes in the solar corona
Problem: Thermodynamics and transport...
• Plasma is multi-component and non-uniform
→ multiple scales and complexity
• Plasma is tenuous and turbulent
→ free energy for microinstabilities→ wave-particle interactions (quasilinear diffusion) → weak collisions (Fokker-Planck operator)→ strong deviations from local thermal equilibrium→ global boundaries are reflected locally→ suprathermal particle populations
Kinetic Vlasov-Boltzmann theory
Description of particle velocity distribution function in phase space:
Relative velocity w, mean velocity u(x,t), gyrofrequency Ω, electricfield E' in moving frame:
Convective derivative:
Moments: Drift velocity, pressure(stress) tensor, heatflux vector
Dum, 1990
Coulomb collisions and quasilinear wave-particle interactions
Coulomb collisions and/or wave-particle interactions arerepresented by a second-order differential operator, including theacceleration vector A(v) and diffusion tensor D(v):
Parameter Chromo -sphere
Corona (1RS)
Solar wind (1AU)
ne (cm-3) 1010 107 10
Te (K) 6-10 103 1-2 106 105
λe (km) 10 1000 107
Quasi-linear pitch-angle diffusion
Diffusion equation
→ Energy and momentum exchange between waves and particles. Quasi-linear evolution.....
Kennel and Engelmann, 1966; Stix, 1992
Superposition of linear waves with random phases!
Pitch-angle gradient in wave frame
Ingredients in diffusion equation
Resonant wave-particle relaxation rate
Marsch, Nonlin. Proc. Geophys. 9, 1, 2002
Corona is weakly collisional, Ωi,e >> νi,e, and strongly magnetized, ri,e << λi,e
Resonant speed, Bessel function of order s
Normalized wave spectrum (Fourier amplitude)
Observation of pitch-angle diffusion
Marsch and Tu, JGR, 106, 8357, 2001
Solar wind protonVDF contours aresegments of circlescentered in the wave frame (ω/k ≤VA )
Velocity-space resonantdiffusion caused by the cyclotron-wave field!
Helios
Numerical simulation of diffusion
Proton velocity distribution from a direct numerical simulation. The phase speeds of the left-hand polarized modes are indicated by the right dots. The five left dots represent the corresponding cyclotron resonance velocities. The corresponding ion diffusion plateaus are indicated by heavy solid lines.
Gary and Saito, JGR, 2003
Semi-kinetic model of wave-ion interaction in the corona
Vocks and Marsch, GRL, 28, 1917, 2001
Reduced Velocity distributions
Marsch, Nonlinear Proc. Geophys., 5, 111, 1998
Transparency of coronal oxygen ions
Plateau formation and marginal stability of the oxygen O5+ VDF at 1.44 Rs
vanishing damping rate
Vocks & Marsch, Ap. J. 568, 1030 , 2002
Model velocity distribution function
Effective perpendicularthermal speed
Velocity distributions of oxygen ions
Vocks & Marsch, Ap. J. 568, 1030 , 2002
r= 1.44 Rs r= 1.73 Rs
Pitch angle scattering, plateau
Magneticmirror force, runaway
Breakdown of classical transport theory
Sun
• Strong heat flux tail
• Collisional free path λc muchlarger than temperature-gradient scale L
• Polynomial expansion abouta local Maxwellian hardlyconverges, as λc >> L
Pilipp et al., JGR, 92, 1075, 1987
solar wind electrons
ne = 3-10 cm-3 Te= 1-2 105 K at 1 AU
Solar wind electrons: Core-halo evolution
Maksimovic et al., JGR, in press 2005
Normalized core remains constantwhile halo is relatively increasing.
Halo is relatively increasingwhile strahl is diminishing.
HeliosWind Ulysses
0.3-0.41 AU
1.35-1.5 AU
Scattering by meso-scale magnetic structures
Spitzer-Härm theory invalid
Dorelli and Scudder, GRL, 1999
For a κ -function (or anyother VDF with moderate non-Maxwellian tails) heat(T0=5 105 K) may flow up the temperature gradient!
Reason: Trapping of low-energy electrons and theresulting velocity filtration.
Rs < r < 1.1 Rsθ = qe/q0sat
Collisional electrons in corona
Pierrard et al., JGR, 2001
• Numerical solution of Boltzmann equation with fullFokker-Planck operator
• Collisions (self- and withprotons) shape pitch-angledistribution.
• Gravitational and electro-staticpotential matter.
• At the lower boundaryMaxwellian, at 14Rs no sunwardelectrons above V2
esc=2eΦE/me.
• Dots: w2=2kBT0/me, i.e. thethermal speed at T0.
steepening
run away
Suprathermal coronal electrons causedby wave-particle interactions I
Vocks and Mann, Ap. J., 593, 1134, 2003
Boltzmannequation withwaves and collisions
A(s) flux tubearea function
Electron pitch-anglescattering in thewhistler wave field
Phase speed vA,e in solar corona
Suprathermal coronal electrons caused bywave-particle interactions II
Vocks and Mann, Ap. J., 593, 1134, 2003
s= 0.014 Rs s= 6.5 Rs
Focusing-> Strahl
Pitch-angle scattering -> shell formation
Protons and cyclotron waves
• Ion core temperature anisotropy(cyclotron resonance)
• Hot ion beams (coronal jets?)
• Loss-cone type distribution
• Parametric decay of large-amplitude Alfvén waves
• Sporadic electron beams maydrive electrostatic ion-cyclotronwaves
Anisotropic isocontours of proton velocity distributions in fast solar wind (Helios)
Do these kinetic processes operate in the corona?
Heat flux generated cyclotron waves
Markovskii and Hollweg, Ap.J., 608, 1112, 2004
• Sporadic heat flux (resonant coreelectrons) drives sunward electrostaticion-cyclotron wave (ω = 1.15 Ωp)
• Intermittent ion heating by waveabsorption (δT/T = 0.07 per burst)
Intermittent (δt = 1 s) electron heat fluxcaused by small-scale reconnection(microflares) at coronal base
Tb = 10Tc nb/nc= 0.15 VA = 3000 km/s ub = VTb
Kinetic Alfvén (compressive ion-cyclotron) waves inferred from radio scattering
Harmon and Coles, JGR, 2005
background
wave compressibility
Radio wave structure function(electric field coherence) relatesto local density fluctuationspectrum.
Inner dissipation scale at proton inertial length:
kD = ωp/c = Ωp/VA
Electron Landau and ioncyclotron damping!
kD-1 = 150 m in coronal
hole
Here τ is the time lag, and ω = ω0 + κ • V.
___ empirical
----- cascade model
Regulation of proton core anisotropy
Marsch et al., J. Geophys. Res., 109, 2004
Empirical least-squares fit of anisotropy versus plasma beta:
T⊥/T⎜⎜ = 1.16 β⎜⎜C(-0.55)
T⊥/T⎜⎜
The core temperature anisotropy isregulated by quasilinear diffusion of protons in resonance with thermal dispersive cyclotron waves!
• Fast solar wind
• V > 600 km/s
• 36297 proton spectra
• Days 23 -114 in 1976
Proton temperature anisotropy and firehose instability
Marsch, Zhao, Tu, Ann. Geophysicae, submitted, 2005
R < 0.4 AU 0.4 AU < R < 1 AU
A = 1- T⊥ / T⎜⎜
core
beam
Stability of solar wind proton beams
Tu et al., J. Geophys. Res., 109, 2004
Plot of drift speed versus plasma beta, Vd/VA = 2.16 β 0.28 , indicates stability!
• Well resolved beams
• 616 proton spectrathreshold
• Origin of the proton beam not yetexplained; collisions or waves?• Proton beam speed is regulated bywave-particle interactions!
Conclusions
• Classical transport theory for ions and electrons breaks down already low in the solar corona and even more so in the solar wind.
• Electron heat conduction is not well understood in the presence of whistler turbulence, collisional run-away and electrons being trapped in or escaping from the electrostatic (gravitational) potential.
• Kinetic physics including wave-particle interactions adequately describes key non-thermal features of solar wind ions, but a turbulent wave transport theory (coefficients) for the corona does not yet exist.
• Viscous, ohmic and conductive (collisional) heating are insufficient, however a simple rescaling of transport coefficients is not meaningful.
• The thermodynamics (heating) of the solar corona will ultimately require a kinetic plasma approach to understand the dissipation.